The probability that A can solve a problem is 7/12 and for B it is 9/17. If both of them try independently, then the probability that the problem is solved is

Correct Answer is : 415141/515141

Correct Answer is : 415141/515141

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AP ICET 2016 Paper

Question : 142 of 200

Marks: +1, -0

\frac{7}{12}

\frac{9}{17}

Solution:

Given :

p(A)=\frac{7}{12},p(B)=\frac{9}{17}

\Rightarrow P(\overline{A})=\frac{5}{12},p(\overline{B})=\frac{8}{17}

Probability that A and B can’t solve the problem

=p(\overline{A})\times p(\overline{B})

Probability that the problem is solved.

= 1 – probability that A and B can’t solve the problem.

=1-[p(\overline{A})\times p(\overline{B})]

=1-\left(\frac{5}{12}\times\frac{8}{17}\right)=1-\frac{10}{51}=\frac{41}{51}

Aliter : Problem can be solved in either of the following three cases :(i) A solves but not B (ii) B solves but not A (iii) Both A and B solve.

∴ Required probability

=p(A)\cdot p(\overline{B})+p(\overline{A})\cdot p(B)+p(A)\cdot(p(B)

=\left(\frac{7}{12}\times\frac{8}{17}\right)+\left(\frac{5}{12}\times\frac{9}{17}\right)+\frac{7}{12}\times\frac{9}{17})

=\frac{56+45+63}{12\times 17}=\frac{164}{12\times 17}=\frac{41}{53}

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